How to disable iMessage on a broken iPhone?

The simplest solution is to contact Apple Support (as this article makes clear) since they actually have engineers that can modify which devices and phone numbers are associated with your (or another's Apple ID).

So, just contact Apple Support.

Try to log in to your iPhone with her Apple ID and turn off the settings for iMessage there. Worst case you need to insert her SIM card into your phone and do the changes.

I ran into this same issue, not with a broken iPhone though. I have a Nexus 5 to replace my old iPhone 4. My wife's texts to me from her iPhone kept going as iMessages.

I found this article that helped me solve the problem.

Note: If you no longer have access to the iPhone that is using the number you want to remove, reset your Apple ID password.

http://support.apple.com/kb/HT5538

What I did was disable facetime and iMessage on my phone (with no sim). Changed my apple ID password. After this texts worked again to me.